自然科学版
陕西师范大学学报(自然科学版)
数学与计算机科学
连续Quantale及其范畴性质
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梁少辉,赵彬
(陕西师范大学 数学与信息科学学院, 陕西 西安 710062)
梁少辉,男,博士研究生,研究方向为格上拓扑与模糊推理.
摘要:
研究了连续Quantale及其范畴性质,定义了半连续Quantale,在此基础上讨论了半连续Quantale、连续Quantale和正则Quantale之间的关系.证明了严格右侧的连续Quantale是正则Quantale,严格右侧的左侧Quantale是连续Quantale当且仅当它是半连续Quantale.给出了连续Quantale中理想的概念,探讨了连续Quantale中理想和连续Quantale范畴的性质,证明了此范畴不仅是点化的、连通的,而且有乘积、每一个投射都是收缩.
关键词:
半连续Quantale; 理想; 连续Quantale同态; 范畴
收稿日期:
2007-12-15
中图分类号:
O153.1
文献标识码:
A
文章编号:
1672-4291(2008)05-0001-05
基金项目:
国家自然科学基金资助项目(10471083);教育部高校优秀青年教师教学科研奖励计划基金资助项目([2000]26)
Doi:
Continuous quantales and its category properties
LIANG Shao-hui, ZHAO Bin
(College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China)
Abstract:
Some properties of continuous quantales and the category of continuous quantales are studied,the definition of semicontinuous quantale is given, the relations of semicontinuous quantale, regular quantale and continuous quantale are then discussed. It is proved that a continuous quantale is regular when it is a strictly right-side quantale and that a strictly right-side left quantale is continuous if and only if it is a semicontinuous quantale. The concept of the ideal of a continous quantale is given. Some properties of the category of continuous quantales are discussed, it is proved that the category of continuous quantales is pointed and connected has a product, and that each projection of the category of continous quantales is a retract.
KeyWords:
semicontinuous quantale; ideal; continuous quantale homomorphism; category